When I get to the end of my TOS ongoing marathon I'm going to do my best to figure out if I can wiggle around the issue. The presence of female captains in Vanguard, presumably set before this ep, put a lie to the whole thing anyways.

The easiest fix is to assume that Lester was paranoid and deluded and Kirk was just playing along with the delusion because he knew it was pointless to try to reason with her.